What can be inferred from limited clinical data by using current models of hepatic elimination? We examined this question by analyzing previously published data on the steady-state uptake of the anticancer agent 5-fluorouracil (5-FU) in seven cancer patients in terms of the venous equilibration model, the undistributed and distributed forms of the sinusoidal perfusion model, and the convection-dispersion model. Because of appreciable extrasplanchnic removal of 5-FU, the value of the steady infusion rate was not used in our analysis. When the data from all patients were pooled by plotting the measured hepatic venous concentration against the measured hepatic arterial concentration, the high concentration data fell on a limiting straight line of slope 1, indicating that at high dose rates elimination of 5-FU in both the liver and gastrointestinal tract was close to saturation. The intercept of this line gave a model-independent estimate of Vmax/Q = 48.0 +/- 11.6 (SD) microM for the pooled data set, where Vmax is the maximum splanchnic elimination rate of 5-FU, and Q is the hepatic blood flow. The low concentration data points fell on a limiting straight line through the origin, from which model-dependent values of the Michaelis constant were determined. The venous equilibration model gave Km = 9.4 microM, while the undistributed sinusoidal perfusion model gave Km* = 26.5 microM. With these values of Km, both models fit the pooled data equally well. These methods were applied to analyses of the five individual data sets which contained sufficiently high concentration data points. The resulting mean values were Vmax/Q = 41.0 +/- 5.1 (sem) microM, Km = 8.4 +/- 1.3 microM and Km* = 23.2 +/- 3.2 microM. However, the splanchnic region is a highly heterogeneous organ system, for which an undistributed analysis provides no more than an upper bound on the Michaelis constant Km+ (Km+ less than or equal to Km*). A perfusion model distributed to represent total splanchnic elimination is developed in the Appendix. Using previous estimates of the degree of functional heterogeneity in the liver alone, this model yields Km+ values for individual patients which have a mean of 20.3 +/- 2.8 microM.